Wright took Chester back into League Two as Conference champions last year but honours on the day went to opposite number Keith Curle, the man who only moved into the City hot seat for the final game of last season.
After a delayed start due to congestion at the turnstiles, the opening half was surprisingly ill-tempered with referee Matt Messias showing yellow cards to Chester pair Ben Davies and Tom Curtis, plus Posh's Paul Carden.
Chances were almost non-existent apart from an early rising shot by Ryan Lowe which needed smart handling by Mark Tyler in the home goal, and a snap effort from Posh defender Sagi Burton that dipped just over Chris McKenzie's crossbar.
Parading five of his seven summer signings, Posh boss Wright looked to have injected fresh impetus into his side with a second half switch from five at the back to a 4-4-2 formation following the introduction of livewire teenage winger Ryan Semple.
But as the game opened up it was Chester who broke out of defence with Ben Davies sweeping over a right-wing cross that caused all sorts of problems in the Posh defence before one-time Morecambe marksman Drummond confidently hooked the ball past a poorly protected Tyler.
Posh chased the game, bringing on another youngster in Jamie Day, and former Norwich front man Danny Crowe looked set to equalise after beating McKenzie, only to see the shot cleared from the goal line.
Then McKenzie flung himself to keep out a shot from Burton that looked to be heading for the top corner of the net.